A363698 a(n) = n! * Sum_{d|n} (-1)^(d+1) * (n/d)^n / d!.

1, 7, 163, 5951, 375001, 33337559, 4150656721, 675135713279, 140588337476161, 36270281280965759, 11388728893445164801, 4270306368140557557119, 1886009588552176549862401, 968696203690612910273080319

Offset: 1

Author

Seiichi Manyama, Jun 16 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..232

Crossrefs

Cf. A132958, A363697.

Cf. A354892.

Programs

Mathematica

a[n_] := n! * DivisorSum[n, (-1)^(#+1) * (n/#)^n / #! &]; Array[a, 15] (* Amiram Eldar, Jul 03 2023 *)

PARI

a(n) = n!*sumdiv(n, d, (-1)^(d+1)*(n/d)^n/d!);

Formula

E.g.f.: Sum_{k>0} (1 - exp(-(k * x)^k)).

If p is prime, a(p) = (-1)^(p+1) + p^p * p!.